Preheat the oven to 400°F. Toss the sweet potatoes with the olive oil, salt, and pepper and spread out on a large rimmed baking sheet. Roast until tender when pierced with a fork, about 25 minutes. Remove from the oven and set aside.
Melt 2 TBS of the coconut oil over medium heat in a large saucepan. Add the onion and saute until translucent, about 3 minutes. Add the turmeric, curry powder, and ginger and saute until fragrant, 2 minutes more. Add the roasted sweet potato and broth and bring to a boil, then reduce heat to a simmer. Simmer for 20 minutes, then remove from heat and carefully transfer to a blender. Add the orange juice and coconut milk and blend until very smooth. Season to taste with salt and pepper. Set soup aside.
In a small frying pan, melt the remaining 1 TBS of coconut oil over medium heat. Add the shallots and saute until translucent, about 2 minutes. Add the cooked lentils and saute until crispy, another 2 minutes. Remove from the heat.
Scoop a 1/2 cup of brown rice into each bowl. Pour soup over the rice, then top with lentils, yogurt, and cilantro.